A car retailer thinks that a 40,000-mile claim for tire life b y the manufacturer is too high. She carefully records the mileage obtained from a sample of 64 such tires. The mean turns out to be 38,500 miles. The standard deviation of the life of all tires of this type has previously been calculated by the manufacturer to be 7,600 miles. Assuming that the mileage is normally distributed, determine the largest signifi cance level at which we would accept the manufacturer’s mileage claim, that is, at which we would not conclude the mileage is signifi cantly less than 40,000 miles.

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